On the morning of April 25, 2005, a JR West commuter train came into Itami station too fast and stopped about 72 meters past its mark.
The intercom from the driver’s cab rang. The conductor later recalled something like “can you knock it down a bit?” and understood: report a shorter overrun. Then the conductor radioed the control center. To the conductor, the overrun had felt like 30 or 40 meters. But the conductor had heard that about 5 meters meant no harsh punishment for a driver, and 5 seemed too few to be believed.
“Eight meters,” the conductor said. The dispatcher read the number back.
Beads in a box
The American statistician W. Edwards Deming staged a game in his management seminars to show why reward and punishment so often land on the wrong person. The account here follows the statistician Sharon Lohr’s 2015 description of it, which quotes Deming’s seminars and books.
The game needs a box of beads, 800 red and 3,200 white, and a paddle with 50 small holes. A few volunteers from the audience become “willing workers.” Their job is to make white beads; red ones are defects. Each worker dips the paddle into the box, following the procedure exactly.
Inspectors count the red beads in each paddle. Then the foreman, played by Deming, gets to work. Workers with few red beads get merit raises. Workers with 12 or more go on probation. “If he makes any red beads, see how he did it,” he would tell the others. “Make sure you don’t do it.”
The game runs for four “days.” In one seminar, recorded in the book Four Days with Dr. Deming, a worker named Sue drew 7 red beads on the first day, 8 on the second and 13 on the third. “Sue just got careless,” Deming said. “It sometimes happens after a merit raise. But I like her attitude.”
Nothing Sue did changed the box. The differences between workers were luck, everyone in the room understood that, and the workers were frustrated anyway.
The Deming Institute sums up the lesson: even a willing worker who wants to do a good job is “directly tied to and limited by the nature of the system they are working within.” In the game, where the box decides everything, real improvement can only come from changing the box, and praise and punishment just rearrange who looks lucky. Real work is rarely that strict, but the game shows how easily luck passes for skill.
Fear and false figures
The game has a darker variation. In 2010 one instructor, reported by the statistician Sharon Lohr, told the workers they would be fired for any paddle with five or more red beads, then moved the box out of sight. Every time he ran it, the workers came back with fewer than five, and none reported breaking the procedure. His conclusion: workers whose jobs are on the line can improve the system, distort the system, or distort the data.
Lohr quotes Deming putting it more bluntly: “Fear invites wrong figures…. To keep his job, anyone may present to his boss only good news.”
The conductor’s “8 meters” was a distorted figure, given for exactly that reason. Investigators concluded the driver was probably working out excuses to match it instead of braking for the next curve. His earlier overruns had led to days off the trains writing essays that were mostly exhortation, with nothing on braking. Yet on some cars of his train’s type, the brake handle could stall between its two strongest positions and apply neither. He had overrun a station that way the year before. The essays were aimed at the worker. One of the red beads was in the cab.
Asking what’s in the box
Imagine a call center that ranks its agents every week by average call length. The bottom five go to a refresher course. Most weeks it is a different five, because who gets the long billing calls is mostly down to the queue. The agents learn the real lesson: end difficult calls early and let customers ring back.
The red bead question is to ask, before you rank anyone, how much of the difference is the box. Start by checking whether the work is comparable at all: did everyone get the same mix of calls? Then plot the numbers over time on a proper control chart, which shows how much results vary when nothing unusual is going on. A point outside those limits is a signal worth investigating. The cause might be a person, or a broken headset, bad call routing or a recording error. And results inside the limits don’t prove everyone is equally good; steady differences can still be there. The limits alone just can’t rank people.
Red beads in the evals
AI work has its own box of beads. When two models or two prompts are compared on a test, part of the gap can be the questions that happened to be chosen and the randomness in the model’s answers. Anthropic’s researchers put it plainly in 2024: one model might “simply have gotten lucky in the choice of questions.” They recommend reporting the margin of error with every score, and, for models that reason step by step, asking each question several times and averaging, which reduces the randomness in the answers. When two models answer the same questions, they suggest comparing them question by question and looking at the error on those differences, for a sharper estimate of how uncertain the gap is.
A team that runs ten prompt versions once each and crowns the top scorer may be playing the red bead game with software. Picking the highest of ten scores on the same questions tends to pick a version that was lucky on exactly those questions, so the winning score probably flatters it. Before trusting it, test it on fresh questions that played no part in the choice and resemble its real work.